Annulus

Two concentric circles form an annulus of width 10 cm. The radius of the smaller circle is 20 cm. Calculate the content area of annulus.

Result

S =  1570.796 cm2

Solution:

r2=20 cm m=10 cm r1=r2+m=20+10=30 cm  S1=π⋅ r12=3.1416⋅ 302≐2827.4334 cm2 S2=π⋅ r22=3.1416⋅ 202≐1256.6371 cm2  S=S1−S2=2827.4334−1256.6371≐1570.7963≐1570.796 cm2r_{ 2 }=20 \ \text{cm} \ \\ m=10 \ \text{cm} \ \\ r_{ 1 }=r_{ 2 }+m=20+10=30 \ \text{cm} \ \\ \ \\ S_{ 1 }=\pi \cdot \ r_{ 1 }^2=3.1416 \cdot \ 30^2 \doteq 2827.4334 \ \text{cm}^2 \ \\ S_{ 2 }=\pi \cdot \ r_{ 2 }^2=3.1416 \cdot \ 20^2 \doteq 1256.6371 \ \text{cm}^2 \ \\ \ \\ S=S_{ 1 } - S_{ 2 }=2827.4334 - 1256.6371 \doteq 1570.7963 \doteq 1570.796 \ \text{cm}^2

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